Advertisements
Advertisements
Question
In the figure given below, Ray PT is bisector of ∠QPR. If PQ = 5.6 cm, QT = 4 cm and TR = 5 cm, find the value of x .
Solution
Given: ray PT is bisector of ∠QPR.
PQ = 5.6 cm, QT = 4 cm and TR = 5 cm.
In a triangle, the angle bisector divides the side opposite to the angle in the ratio of the remaining sides.
`"QT"/"TR"="PQ"/"PR"`
`4/5=5.6/x`
`x=(5.6xx5)/4`
`x=28/4=7`
`PR=7cm`
APPEARS IN
RELATED QUESTIONS
In figure, find ∠L
Examine each pair of triangles in Figure, and state which pair of triangles are similar. Also, state the similarity criterion used by you for answering the question and write the similarity relation in symbolic form
figure (i)
figure 2
figure 3
figure 4
figure 5
figure 6
figure 7
The diagonal BD of a parallelogram ABCD intersects the segment AE at the point F, where E is any point on the side BC. Prove that DF × EF = FB × FA
`triangleDEF ~ triangleMNK`. If DE = 5 and MN = 6, then find the value of `(A(triangleDEF))/(A(triangleMNK))`
E and F are the points in sides DC and AB respectively of parallelogram ABCD. If diagonal AC
and segment EF intersect at G; prove that:
In triangle ABC, AD is perpendicular to side BC and AD2 = BD × DC. Show that angle BAC = 90°.
In the given figure, DB⊥BC, DE⊥AB and AC⊥BC.
Prove that `(BE)/(DE)=(AC)/(BC)`
In a right triangle ABC, right angled at B, D is a point on hypotenuse such that BD ⊥ AC , if DP ⊥ AB and DQ ⊥ BC then prove that
`(a) DQ^2 Dp.QC (b) DP ^2 DQ.AP 2 `
The areas of two similar triangles ABC and PQR are in the ratio 9:16. If BC = 4.5cm, find the length of QR.
In the given figure, DE║BC. If DE = 3cm, BC = 6cm and ar(ΔADE) = `15cm^2`, find the area of ΔABC.
If Δ ABC , MN || BC .
If AN : AC= 5 : 8, find ar(Δ AMN) : ar(Δ ABC)
In Δ ABC , MN || BC .
If `"AB"/"AM" = 9/4` , find `("Ar" ("trapezium MBCN"))/("Ar" . (triangle "ABC"))`
In MBC, DE is drawn parallel to BC. If AD: DB=2:3, DE =6cm and AE =3.6cm, find BC and AC.
A line segment DE is drawn parallel to base BC of ΔABC which cuts AB at point D and AC at point E. If AB = 5BD and EC = 3.2 cm, find the length of AE.
Sides of a triangle are 7, 24 and 25. Determine whether the triangle is a right-angled triangle or not.
In ΔABC, point D divides AB in the ratio 5:7, Find: `"AE"/"EC"`
In ΔABC, point D divides AB in the ratio 5:7, Find: `"AE"/"AC"`
Find the scale factor in each of the following and state the type of size transformation:
Image length = 8cm, Actual length = 20cm.
ΔPQR ~ ΔSUV. Write pairs of congruent angles
Two triangles are similar. Smaller triangle’s sides are 4 cm, 5 cm, 6 cm. Perimeter of larger triangle is 90 cm then find the sides of larger triangle.
