The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased
by x cm and its width is increased by x cm, its area is increased by 35 sq. cm.
a. Express the new length and the new width in terms of x.
b. Express the new area of the rectangle in terms of x.
c. Find the value of x.
Calculate the current area. Using our rectangle calculator with length = 30 and width = 18, we get:
A = 540
a) Decrease length by x and increase width by x, and we get:
(30 - x)(18 + x) = 540 + 35
Multiplying through and simplifying, we get:
540 - 18x + 30x - x^2 = 575
-x^2 + 12x + 540 = 575
c) We have a quadratic equation. To solve this, we type it in our search engine, choose solve, and we get:
x = 5 or x = 7
Trying x = 5, we get:
A = (30 - 5)(18 + 5)
A = 25 * 23
A = 575
Now let's try x = 7:
A = (30 - 7)(18 + 7)
A = 23 * 25
A = 575
They both check out.
So we can have
by x cm and its width is increased by x cm, its area is increased by 35 sq. cm.
a. Express the new length and the new width in terms of x.
b. Express the new area of the rectangle in terms of x.
c. Find the value of x.
Calculate the current area. Using our rectangle calculator with length = 30 and width = 18, we get:
A = 540
a) Decrease length by x and increase width by x, and we get:
- length = 30 - x
- width = 18 + x
(30 - x)(18 + x) = 540 + 35
Multiplying through and simplifying, we get:
540 - 18x + 30x - x^2 = 575
-x^2 + 12x + 540 = 575
c) We have a quadratic equation. To solve this, we type it in our search engine, choose solve, and we get:
x = 5 or x = 7
Trying x = 5, we get:
A = (30 - 5)(18 + 5)
A = 25 * 23
A = 575
Now let's try x = 7:
A = (30 - 7)(18 + 7)
A = 23 * 25
A = 575
They both check out.
So we can have