MATH SOLVE

3 months ago

Q:
# Sketch a rectangle and label its dimensions that meets the following conditions perimeter 18 area 20

Accepted Solution

A:

Answer: 4 units by 5 unitsStep-by-step explanation:To solve this problem, then we must develop two equations; one for the perimeter and another for the area of the rectangle.
The perimeter of a rectangle = 2(L +B)
The area of a rectangle = L x B
Let the length be represented by L while the breadth is denoted by B. Then, our equations are
2L + 2B =18 --- eq 1
and LB = 20 ----- eq 2
From eq 2, then L = 20/B
We shall substitute this in equation 1 such that
2(20/B) + 2B =18
= 40/B + 2B = 18
= 40/B + 2B/1 = (40 + 2B^2) /B =18
We do cross multiplication by multiplying both sides of the equation by B.
We get
40 + 2B^2 = 18B
We then rearrange the equation as 2B^2- 18B + 40 = 0
Dividing both sides by 2, we get B^2- 9B =20 =0
We shall get the roots of the equation to be -4 and -5. Why? -4B-5B =-9 and -4x-5 =20
Thus, B^2- 9B =20 =0 can be reworked as (B-4) (B-5)= 0 From B-4=0, B= 4
From LB =20, If B =4, then L =20/4 = 5
From B-5=0; B=5
From LB =20, If B=5, L = 20/5 = 4
Thus, the dimensions of the rectangle are 5 units and 4 units.