Question

If the area of the red and blue square are 576 cm2 and 256 cm2 respectively, what is the area of the
right angle triangle (in cm2) formed?​

Answer 1

Answer:

side of red square=24cm

side of square = 16cm

and third side of triangle =1/2×16×17.89

=8×17.89=143.1cm^2

Answer 2

Given,

The area of the red square = 576 cm2

The area of the blue square = 256 cm2

To find,

The area of the right-angled triangle (in cm2) formed.

Solution,

We can simply solve this mathematical problem using the following process:

As per mensuration;

The area of a square

= (length of each side)^2

Area of a right-angled triangle

= 1/2 × (base) × (height)

Now, according to the question;

The area of the red square

= 576 cm2 = (24 cm)^2

=> length of each side of the red square = 24 cm

And, the area of the blue square

= 256 cm2 = (16 cm)^2

=> length of each side of the blue square = 16 cm

Now, according to the figure;

The hypotenuse of the right-angled triangle formed

= length of each side of the red square

= 24 cm

The height of the right-angled triangle formed

= length of each side of the blue square

= 16 cm

Let us assume that the length of the base of the right-angled triangle formed is x cm.

Now, on applying Pythagoras theorem in the right-angled triangle formed, we get;

(base)^2 + (height)^2 = (hypotenuse)^2

=> x^2 + (16 cm)^2 = (24 cm)^2

=> x^2 = 576 cm2 - 256 cm2 = 320 cm2

=> x = 8√5 cm

=> length of the base = 8√5 cm

Now, the area of the right-angled triangle formed

= 1/2 × (base) × (height)

= 1/2 × (8√5 cm) × (16 cm)

= 64√5 cm2

= 143.1 cm2

Hence, the area of the right-angled triangle formed is equal to 64√5 cm2, that is, 143.1 cm2.