Find the sidelength of a rhombus whose diagonals are of length 24 units and 70 units. Class 8

Find the sidelength of a rhombus whose diagonals are of length 24 units and 70 units. Class 8

Question 1.

Find the sidelength of a rhombus whose diagonals are of length 24 units and 70 units. Class 8

Solution:

ABCD is a rhombus.

It diagonal intersect at O.

So, OA = OC = 12 cm ([latex]\frac{1}{2}[/latex] × 24)

and OB = OD = 35 cm ([latex]\frac{1}{2}[/latex] × 70)

Further, ∠AOB = 90°.

So, AB² = OA² + OB²

= 12² + 35².

= 144 + 1225 = 1369.

Hence, sidelength of the rhombus

= [latex]\sqrt{1369}[/latex] cm = 37 cm.

Question 2.

Is the hypotenuse the longest side of a right triangle? Justify your answer. Class 8

Solution:

Yes. Sum of two squares (positives) will be greater than the square of each other side of the triangle.

Question 3.

True or False — Every Baudhayana triple is either a primitive triple or a scaled version of a primitive triple. Class 8

Solution:

True.