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Wewaii [24]
3 years ago
9

One of diagonals of a parallelogram is its altitude. What is the length of this altitude, if its perimeter is 50 cm, and the len

gth of one side is 1 cm longer than the length of the other?

Mathematics
1 answer:
Otrada [13]3 years ago
7 0

The length of that altitude is 5 cm.

<em><u>Explanation</u></em>

According to the below diagram, ABCD is a parallelogram with diagonal \overline{AC} as its altitude.

Suppose, the length of side \overline{AB} is x cm.

As the <u>length of one side is 1 cm longer than the length of the other</u>, so the length of side \overline{BC} will be: (x+1) cm

Given that, the perimeter of the parallelogram is 50 cm. So, the equation will be.....

2[x+(x+1)]=50\\ \\ 2(2x+1)=50\\ \\ 4x+2=50\\ \\ 4x=48\\ \\ x= 12

So, the length of \overline{AB} is 12 cm and the length of \overline{BC} is (12+1)= 13 cm.

Suppose, the length of the altitude(\overline{AC}) is h cm.

Now, in right angle triangle ABC, using <u>Pythagorean theorem</u>....

(AC)^2+(AB)^2= (BC)^2\\ \\ h^2+(12)^2= (13)^2\\ \\ h^2+144= 169\\ \\ h^2= 25\\ \\ h= \sqrt{25}= 5

So, the length of that altitude is 5 cm.


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