In Delta ABC, a line through A cuts the side | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Triangles $\Delta ABD$ and $\Delta ADC$ share the same vertex $A$ and their bases $BD$ and $DC$ lie on the same line $BC$.Therefore,they have the

Vedclass · Accepted Answer

$75$

Vedclass · Answer

(C) Triangles $\Delta ABD$ and $\Delta ADC$ share the same vertex $A$ and their bases $BD$ and $DC$ lie on the same line $BC$.Therefore,they have the same height $h$ from vertex $A$ to the base $BC$.The area of a triangle is given by $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Area of $\Delta ABD = \frac{1}{2} 	imes BD 	imes h = 60 \, cm^2$.Given $BD : DC = 4 : 5,$ let $BD = 4x$ and $DC = 5x$.So,$\frac{1}{2} 	imes 4x 	imes h = 60 \implies 2xh = 60 \implies xh = 30$.Now,Area of $\Delta ADC = \frac{1}{2} 	imes DC 	imes h = \frac{1}{2} 	imes 5x 	imes h$.Substituting $xh = 30$,we get Area of $\Delta ADC = \frac{1}{2} 	imes 5 	imes (xh) = \frac{1}{2} 	imes 5 	imes 30 = 75 \, cm^2$.

In $\Delta ABC,$ a line through $A$ cuts the side $BC$ at $D$ such that $BD : DC = 4 : 5.$ If the area of $\Delta ABD = 60 \, cm^2,$ then the area of $\Delta ADC$ is......$cm^2$.

Similar Questions

Two circles touch internally. The sum of their areas is $116\, \pi \, cm^2$ and the distance between their centers is $6 \, cm$. Then,the radii of the circles are?

What will be the cost of gardening a $1 \text{ m}$ broad boundary around a rectangular plot having a perimeter of $340 \text{ m}$ at the rate of $₹ 10$ per square metre?

$A$ drawing room is $7.5 \text{ m}$ long,$6.5 \text{ m}$ broad,and $6 \text{ m}$ high. Find the length of paper $2.5 \text{ dm}$ wide required to cover its walls,allowing $8 \text{ m}^2$ for doors.

The ratio of bases of two triangles is $x: y$ and that of their areas is $a: b$. Then the ratio of their corresponding altitudes will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module