Question

AABC is a right-angled isosceles triangle right angled at B such that AB = 4 cm. If D and E are points on BC and AB respectively such that BD = BE = 3 cm, then the value of (AD * CE + AC2) (in sq. cm) is ​

Answer 1

Given:

ABC is a right-angled isosceles triangle right angled at B such that AB = 4 cm. If D and E are points on BC and AB respectively such that BD = BE = 3 cm

To Find:

the value of (AD * CE + AC2) (in sq. cm) is ​

Solution:

Let us draw a diagram to solve the question more easily, construct a right-angled triangle ABC right angled at B with sides AB=BC=4cm, now plot two points D and E on lines BC and AB respectively.

Now we can continue with the sum, we need to find the value of AD, CE and AC. So,

The value of AD can be found by using the Pythagoras theorem in the triangle ABD

$AD^2=AB^2+BD^2\\AD^2=4^2+3^2\\AD^2=16+9\\AD=\sqrt{25} \\=5cm$

The value of CE can be found by using the Pythagoras theorem in the triangle EBC

$CE^2=EB^2+BC^2\\CE^2=3^2+4^2\\=9+16\\CE=\sqrt{25}\\=5cm$

The value of AC can be found by using the Pythagoras theorem in the triangle ABC

$AC^2=AB^2+BC^2\\=4^2+4^2\\AC=4\sqrt{2} cm$

Now finding the value

$=AC*CE+AC^2\\=5*5+32\\=25+32\\=57cm^2$

Hence, the value of (AD * CE + AC2) (in sq. cm) is ​57 sq.cm