One side of a rectangle is 8cm and the diagonal is 10cm. What is the area of the rectangle?

GoddyJR

6 years ago

From the diagram of a rectangle, a diagonal divides the rectangle into two right angle triangles. Detach one right angle; from the diagram of the detached right angled triangle, the hypotenuse is the diagonal=10cm and the one other side is given as 8cm
.
Recall: Pythagoras theorem
C²=a²+b² where C is the hypotenuse
so let a=8cm
10²=8²+b²
100=64+b²
b²=100-64
b²=36
b=√36
b=6cm
.
but area of a rectangle=L×B=8×6=48cm²
.
sorry i made mistake in the first comment
I hope this goes a long way!

GoddyJR

6 years ago

From the diagram of a rectangle, a diagonal divides the rectangle into two right angle triangles. Detach one right angle; from the diagram of the detached right angled triangle, the hypotenuse is the diagonal=10cm and the one other side is given as 8cm
.
Recall: Pythagoras theorem
C²=a²+b² where C is the hypotenuse
so let a=8cm
10²=8²+b²
100=64+b²
b²=100-64
b²=36
b=√36
b=48cm
.
I hope this goes a long way!

Ooocadif

1 year ago

Let's use the Pythagorean theorem to find the length of the other side of the rectangle:

Diagonal² = Length² + Width²
10² = Length² + 8²
100 = Length² + 64
Length² = 36
Length = √36 = 6cm

Now that we have the length and width, we can find the area:

Area = Length × Width
= 6cm × 8cm
= 48cm²

The correct answer is:

B. 48cm²

ProjectStar

2 months ago

yes

Ooocadif

1 year ago

One side of a rectangle is 8cm and the diagonal is 10cm. What is the area of the rectangle?
A. 80cm2
B. 48cm2
C. 40cm2
D. 36cm2
E. 24cm2
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