Question

Please I really need help! I will mark you as brainliest if the answer is correct!

Answer 1

Given:

PQRS is a rectangle and XY is parallel to PS.

RY = 9 cm, QR = a cm and YS = b cm

Area of PQRS = 84 cm²

Area of PXYS = 21 cm²

To find:

The value of a and b.

Solution:

RS = 9 + b

Area of rectangle = length × width

Area of PQRS = QR × RY

QR × RS = 84

$a \times (9 + b) = 84$

$9a+ab=84$ ----------- (1)

Area of PXYS = XY × PS

XY × PS = 21

$a\times b=21$ (since QR = XY)

$ab=21$ ----------- (2)

Substitute (2) in (1).

$9a+21=84$

Subtract 21 from both sides, we get

$9a = 63$

Divide by 9 on both sides, we get

a = 7

Substitute a = 7 in (2).

$7 b=21$

Divide by 7 on both sides, we get

b = 3

The value of a is 7 cm and b is 3 cm.