Question

Ratio of the area of triangle WXY to the area of triangle WZY is 3:4 .If the area of triangle is 56 sq cm, then find the length of XY and YZ.

Answer 1

Answer:

Let the sides be 3x,4x and 5x. Perimeter= 3x+4x+5x 144=12x X=12 Sides- 36,48,60  Pls mark it the brainliest

Step-by-step explanation:

Answer 2

Answer:

The measure of length of side XZ is 14 square centimeter

The measure of the length of the side YZ is 8 centimeters

Step-by-step explanation:

Given as :

The ratio of area of triangle WXY to the area of triangle WZY = 3 : 4

I.e Area Δ WXY : Area Δ WZY = 3 : 4

Or, $\dfrac{Area \Delta WXY}{Area \Delta WZY}$ = $\dfrac{3}{4}$              .........1

Again

The Area of Triangle WXZ = 56 square centimeter

I.e Area Δ WXZ = 56 sq cm

Again

The measure of height WY = 8 cm

For Area Δ WXZ = $\dfrac{1}{2}$ × height × base

Or, 56 sq cm = $\dfrac{1}{2}$ × WY × XZ

Or, WY × XZ = 56 × 2

Or, 8 × XZ = 112

∴  XZ = $\dfrac{112}{8}$

i.e XZ = 14  cm

So, the measure of length of side XZ = 14 square centimeter

Again

For Area Δ WZY = $\dfrac{1}{2}$ × height × base

i.e  Area Δ WZY =  $\dfrac{1}{2}$ × WY × YZ

From eq 1

$\dfrac{Area \Delta WXY}{Area \Delta WZY}$ = $\dfrac{3}{4}$

So, $\frac{\frac{1}{2}\times XY\times WY}{\frac{1}{2}\times YZ\times WY}$ =  $\dfrac{3}{4}$

Or, $\dfrac{XY}{YZ}$ =  $\dfrac{3}{4}$

Or, $\dfrac{XZ - YZ}{YZ}$ =  $\dfrac{3}{4}$

Or, $\dfrac{XZ}{YZ}$ =  $\dfrac{3}{4}$  + 1

Or, , $\dfrac{XZ}{YZ}$ = $\dfrac{3 + 4}{4}$

Or, , $\dfrac{XZ}{YZ}$ = $\dfrac{7}{4}$

Or, $\dfrac{14}{YZ}$ = $\dfrac{7}{4}$

∴ YZ = $\frac{4\times 14}{7}$

or, YZ = 4 × 2

Or, YZ = 8 cm

So, The measure of the length of the side YZ = 8 centimeters

Hence, The measure of length of side XZ is 14 square centimeter and The measure of the length of the side YZ is 8 centimeters . Answer