Advertisements
Advertisements
Question
In a right-angled triangle ABC, if ∠B = 90°, AB - BC = 2 cm; AC - BC = 4 and its perimeter is 24 cm, find the area of the triangle.
Solution
Given, Perimeter of ΔABC = 24cm
⇒ AB + BC + AC = 24cm ....(i)
AB - BC = 2cm ....(ii)
AC - BC = 4cm ....(iii)
Adding (ii) and (iii), we get
AB + AC - 2BC = 6cm
⇒ AB + AC = 6 + 2BC ....(iv)
Substituing (iv) un (i), we get
6 + 2BC + BC = 24
⇒ 3BC = 18
⇒ BC = 6cm
⇒ AB = 2 + BC
= 2 + 6
= 8cm
∴ Area of right-angled ΔABC
= `(1)/(2) xx "BC" xx "AB"`
= `(1)/(2) xx 8 xx 6`
= 24cm2.
APPEARS IN
RELATED QUESTIONS
Find the area of an isosceles triangle ABC in which AB = AC = 6 cm, ∠A = 90°. Also, find the length of perpendicular from A to BC.
Find the area of an equilateral triangle of side 20 cm.
Find the area of the shaded region in the figure as shown, in which DPQS is an equilateral triangle and ∠PQR = 90°.
In a right-angled triangle ABC, if ∠B = 90°, AB - BC = 2 cm; AC - BC = 4 and its perimeter is 24 cm, find the area of the triangle.
Find the area of an isosceles triangle whose perimeter is 50cm and the base is 24cm.
A wire when bent in the form of a square encloses an area of 16 cm2. Find the area enclosed by it when the same wire is bent in the form of an equilateral triangle
The cross-section of a canal is a trapezium in shape. If the canal is 10m wide at the top, 6m wide at the bottom and the area of cross-section is 72 sq.m, determine its depth.
Each of the equal sides of an isosceles triangle is 4 cm greater than its height. If the base of the triangle is 24 cm; calculate the perimeter and the area of the triangle.
In an isosceles triangle, angles opposite to equal sides are ______.
Two line segments are congruent, if they are of ______ lengths.
