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

The diagonals of a rhombus are $12 \ cm$ and $16 \ cm$. The length of one side is.......$cm$

Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of $9856 \, m^{2}$. (in $m$)

The length of a plot is double its width. If a square piece of land of area $150 \, m^2$ occupies $\frac{1}{3}$ area of the plot,then what is the length of the plot? (in $m$)

What is the perimeter of an equilateral triangle whose area is $4 \sqrt{3} \text{ cm}^2$?

The length and breadth of a rectangular piece of land are in the ratio $5:3$. The owner spent ₹ $6000$ for fencing it from all sides at the rate of ₹ $7.50$ per metre. The difference between its length and breadth is (in metres):

Vedclass Test Series

Exam Paper Generator

Online Exam Module