Question

$△$ABC is constructed such that AB = 5 cm, BC = 12 cm and $\angle$B = 90${}^{\circ }$. Then AC${}^2$ = AB${}^2$ + BC${}^2$.

• A. True
• B. False

Answer 1

The correct option is A

True

Step 1:
Draw the base line AB of the length 5 cm.

Step 2:
Measure the angle B with your protractor. Make a mark at 90 degrees and draw a line from B passing through the mark.

Step 3:
Cut an arc of radius 12 cm on the line passing through the point B. The point where this arc cuts the line is the point C.

Step 4:
Draw a line from A to point C, to get the required triangle ABC, as shown below.

From the above construction, we see that length of side AC is 13 cm.

Now, AC${}^2$ = 13${}^2$ = 169 = 25 + 144 = 5${}^2$ + 12${}^2$ = AB${}^2$ + BC${}^2$

Hence the given statement is true.