Home
Class 14
MATHS
If the length of the sides of a triangle...

If the length of the sides of a triangle are in the ratio 4:5:6 and the inradius of the triangle is 3 cm, then the altitude of the triangle corresponding to the largest side as base is :

A

10 cm/30 सेमी.

B

8 cm/8 सेमी.

C

7.5 cm/7.5 सेमी.

D

6 cm/6 सेमी.

Text Solution

Verified by Experts

The correct Answer is:
C
`triangleABC` में माना AB = 4x, BC = 5x तथा CA = 6x तथा OP, OQ तथा OR अंतः त्रिज्या है जिसमें OP `bot` AB, OR `bot` BC, OQ `bot` AC
`triangle` ABC का क्षेत्रफल = `triangle` AOB + `triangle`BOC + `triangleAOC`
= `1/2xx 4x xx 3 + 1/2 5x xx 3 =1/2xx 6x xx 3`
= `1/2xx 3 (4x + 5x + 6x) = (45x)/2`
माना अभीष्ट ऊँचाई = h
`therefore` `triangle`ABC का क्षेत्रफल = `1/2.6x.h` = `(45x)/2`
`therefore` h = `45/6` = 7.5 cm
Promotional Banner

Similar Questions

Explore conceptually related problems

If the lengths of the sides of a triangle are in the ratio 4:5:6 and the inradius of the triangle is 3 cm, then the altitude of the triangle corresponding to the largest side as base is :

The lengths of the sides of a triangle are in the ration 3:4:5 and its perimeter is 144cm. Find the area of the triangle and the height corresponding to the longest side.

The lengths of the sides of a triangle are in the ratio 3 : 4 : 5. Find the area of the triangle if its perimeter is 144 cm.

If length of altitudes of a triangle are 3,4 and 6 units then inradius of the triangle is,

The lengths of sides of a triangle are in the ratiio 2:3:4 . If the perimeter of the triangle is 63 cm, find the lengths of the sides of the triangle.

If the lengths of the sides of a triangle are 3, 5, 7 , then its largest angle of the triangle is

The length of the sides of a triangle are in the ratio 3:4:5 and its perimeter is 144 cm. The area of the triangle is