Balbharati solutions for Geometry (Mathematics 2) [English] 10 Standard SSC Maharashtra State Board chapter 2 - Pythagoras Theorem [Latest edition]

Identify, with reason, if the following is a Pythagorean triplet.
(3, 5, 4)

Identify, with reason, if the following is a Pythagorean triplet.
(4, 9, 12)

Identify, with reason, if the following is a Pythagorean triplet.

(5, 12, 13)

Identify, with reason, if the following is a Pythagorean triplet.
(24, 70, 74)

Identify, with reason, if the following is a Pythagorean triplet.
(10, 24, 27)

Identify, with reason, if the following is a Pythagorean triplet.
(11, 60, 61)

In the given figure, ∠MNP = 90°, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.

In the given figure, ∠QPR = 90°, seg PM ⊥ seg QR and Q–M–R, PM = 10, QM = 8, find QR.

In the given figure. Find RP and PS using the information given in ∆PSR.

For finding AB and BC with the help of information given in the figure, complete following activity.

AB = BC ..........

∴ ∠BAC =

∴ AB = BC = × AC

                 = × `sqrt8`

                 = × `2sqrt2`

                 =

In the given figure, ∠DFE = 90°, FG ⊥ ED, If GD = 8, FG = 12, find (1) EG (2) FD and (3) EF

In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ² = 4PM² – 3PR².

Walls of two buildings on either side of a street are parallel to each other. A ladder 5.8 m long is placed on the street such that its top just reaches the window of a building at the height of 4 m. On turning the ladder over to the other side of the street, its top touches the window of the other building at a height 4.2 m. Find the width of the street.

In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.

In the given figure, seg PS is the median of ∆PQR and PT ⊥ QR. Prove that,

PR² = PS² + QR × ST + `("QR"/2)^2`

In the given figure, seg PS is the median of ∆PQR and PT ⊥ QR. Prove that, 

PQ² = PS² − QR × ST + `(("QR")/2)^2`

In ∆ABC, point M is the midpoint of side BC. If, AB² + AC² = 290 cm², AM = 8 cm, find BC.

In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS² + TQ² = TP² + TR² (As shown in the figure, draw seg AB || side SR and A-T-B)

Out of the following, which is the Pythagorean triplet?

Some question and their alternative answer are given.

In a right-angled triangle, if sum of the squares of the sides making right angle is 169 then what is the length of the hypotenuse?

Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:

Out of the dates given below which date constitutes a Pythagorean triplet?

Some question and their alternative answer are given. Select the correct alternative.

If a, b, and c are sides of a triangle and a² + b² = c², name the type of triangle.

Some question and their alternative answer are given. Select the correct alternative.

Find perimeter of a square if its diagonal is \[10\sqrt{2}\]

Some question and their alternative answer are given. Select the correct alternative.

Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude.

Height and base of a right angled triangle are 24 cm and 18 cm find the length of its hypotenuse

Some question and their alternative answer are given. Select the correct alternative.

 In ∆ABC, AB = \[6\sqrt{3}\] cm, AC = 12 cm, BC = 6 cm. Find measure of ∠A.

Find the height of an equilateral triangle having side 2a.

Do sides 7 cm, 24 cm, 25 cm form a right angled triangle ? Give reason

Find the length a diagonal of a rectangle having sides 11 cm and 60 cm.

Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.

A side of an isosceles right angled triangle is x. Find its hypotenuse. 

In ∆PQR, PQ = √8 , QR = √5 , PR = √3. Is ∆PQR a right-angled triangle? If yes, which angle is of 90°?

Find the length of the side and perimeter of an equilateral triangle whose height is `sqrt3` cm.

∆ABC is an equilateral triangle. Point P is on base BC such that PC = `1/3`BC, if AB = 6 cm find AP.

From the information given in the figure, prove that PM = PN =  \[\sqrt{3}\]  × a

Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.

Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was \[15\sqrt{2}\]

In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:
4(BL² + CM²) = 5 BC²

Sum of the squares of adjacent sides of a parallelogram is 130 sq.cm and length of one of its diagonals is 14 cm. Find the length of the other diagonal.

In ∆ABC, seg AD ⊥ seg BC, DB = 3CD.

Prove that: 2AB² = 2AC² + BC²

In a trapezium ABCD, seg AB || seg DC seg BD ⊥ seg AD, seg AC ⊥ seg BC, If AD = 15, BC = 15 and AB = 25. Find A(▢ABCD)

In the given figure, ∆PQR is an equilateral triangle. Point S is on seg QR such that QS = n\[\frac{1}{3}\] QR.

Prove that: 9 PS² = 7 PQ²