Please help in math : lenght of rectangle is width+7m. and width of this rectangle is 1/3 of lenght. find lenght of rectangle.
please help and explain

L=W+7

W=1/3L

we can substitute the width in the first relation with 1/3L

L=1/3L+7

we move1/3L to the left

L-1/3L=7

we multiply by 3 to remove the denominator

3L-L-21

2L=21

L=21/2=10.5cm

l = (21/2)m

Step-by-step explanation:

Let's call the length l and width as w.

l = w+7m

(1/3)l=w (Plug in the w value into the first equation)

l = (1/3)l+7m (Now, isolate the l)

(2/3)l = 7m (Multiply both sides by 3/2)

l = (21/2)m

Hope this helps!

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240