the width of a rectangle is 12 cm less than the length the perimeter is 156 cm. Find the length and width

1 answer:

4 0

We can write this question as an equation to solve it. Using L for length and W for width we know that

L+L+W+W=perimeter
2L+2W=perimeter

We can put the value of the perimeter into this

2L+2W=156cm

Next, we have to make sure all the terms (letters) are the same so we can solve it. This means we have to rewrite either the length or width in terms of the other.

We know the width is 12cm less than the length, which is the same as saying L-12
Then we substitute this into the equation and solve L

2L+2(L-12)=156
2L+2L-24=156
4L-24=156
4L=180
L=45cm

Next we use this value to find W.
45-12=33
W=33cm

You might be interested in

If ON = 7x - 5, LM = 6x + 4, NM = x + 6, and OL = 8y + 3, find the values of X and Y for which LMNO must be a parallelogram. Ple

Sladkaya [172]

The values of x and y that will make LMNO a parallelogram are: x = 9, y = 1.5.

<h3>Properties of a Parallelogram</h3>

The opposite sides of a parallelogram are parallel to each other and are also of equal lengths.
Diagonals of a parallelogram are congruent to each other and also bisect each other into equal halves.

Therefore:

ON = LM

Substitute

7x - 5 = 6x + 4

Add like terms

7x - 6x = 5 + 4

x = 9

OL = NM

Substitute

8y + 3 = x + 6

Plug in the value of x

8y + 3 = 9 + 6