Question

HELP is a parallelogram, given OE=4 cm and HL is 5 cm more than PE. Find OH

Answer 1

Hint: To solve this type of problem we will use simple logic and some properties of regular geometry. In this question to find the length of OH we first need to find the length OP by applying the concept that HL intersect PE in two equal parts. Then find the PE as it is the sum of OP and OE. Similarly then find the length of HL as per the given condition in the question. And finally find the OH by dividing the length of HL by 2.

Complete step-by-step answer:

Given: A parallelogram HELP having \[OE = 4\] cm and \[HL = PE + 5\]
We know that the diagonals of a parallelogram bisect each other.
 \[\Rightarrow OP = OE = 4\] cm
Now we can write
∴ \[PE = OP + OE\]
Or,
 \[PE = 4 + 4 = 8\] cm
Given: \[HL = PE + 4\]
So
 \[\Rightarrow HL = 8 + 5 = 13\] cm
Now, diagonals of a parallelogram bisect each other.
∴ \[OH = OL = \dfrac{{1}}{2} \times HL = \dfrac{1}{2} \times 13 = 6.5\] cm
So, the correct answer is “ 6.5”.

Note: Parallelogram is a four sided geometry in which all the properties are exactly the same as the rectangle the only difference is that the length of the diagonals are not the same.