Question

In a diagram shown,

PQRS is a rectangle
XY is parallel to PS
RY= 9cm
Area of PQRS = 84cm^2
Area of PXYS = 21cm^2

Work out the values of a and b
You must show all your working.

Answer 1

a = 7 cm

b = 3 cm

Explanation:

The area of a rectangle is the base multiply by the height.

Area of PQRS = a * (9 + b)

9a + ab = 84 Equation (1)

Area of PXYS = a * b

ab = 21 Equation (2)

Substituting equation (2) into (1), we have

9a + 21 = 84

9a = 84 - 21

a = 63/9

a = 7 cm

Substituting the value of "a" in equation (2), we have

7b = 21

b = 21/7

b = 3 cm

Thus,

a = 7 cm

b = 3 cm

Hope this helps!

Answer 2

Since XY is parallel to PS and RY= 9cm, PS=XY=9cm.

Area of PQRS = PS * QR = 9 * a = 84 => a = 9.33cm

Area of PXYS = 9 * b = 21 => b = 2.33cm

Therefore, a=9.33cm and b=2.33cm.

Finding a and b in the rectangular diagram

We are given that PQRS is a rectangle, XY is parallel to PS, RY = 9 cm, area of PQRS = 84 cm², and the area of PXYS = 21 cm².

We need to find the values of a and b.

Step 1: Using parallel lines:

Since XY is parallel to PS and RY = 9 cm, PS = XY = 9 cm.

Step 2: Using area formulas:

The area of PQRS is given by: PS * QR = 84 cm².

Substituting PS = 9 cm, we get: 9 * a = 84 cm².

Solving for a, we get: a = 9.33 cm.

The area of PXYS is given by: PS * YS = 21 cm².

Substituting PS = 9 cm, we get: 9 * b = 21 cm².

Solving for b, we get: b = 2.33 cm.

Therefore, a = 9.33 cm and b = 2.33 cm.

Here is a breakdown of the steps:

PS = XY = 9 cm (parallel lines)

9 * a = 84 cm² (area of PQRS)

a = 9.33 cm (solving for a)

9 * b = 21 cm² (area of PXYS)

b = 2.33 cm (solving for b)