Question

A rectangle has a width of 8 centimeters and an area of 160 square centimeters a similar rectangle has an area of 250 square centimeters. What are the dimensions of the larger rectangle?

Answer 1

we know that
area of rectangle=L*W/2
L is the length side
W is the width side

smaller rectangle
area=160 cm²
W=8 cm
A=W*L-----> L=A/W
L=160/8----> 20 cm

larger rectangle
Area=250 cm²

area larger rectangle/area smaller rectangle=[scale factor]²
so
scale factor²=250/160----> 1.5625
scale factor=√1.5625----> scale factor=1.25

the dimension larger rectangle=scale factor*dimension smaller rectangle

L (larger rectangle)=(1.25)*(20)---> 25 cm
W (larger rectangle)=(1.25)*8----> 10 cm

the answer is
the dimensions of the larger rectangle are 10 cm x 25 cm