Rectangle Area Problem: Using 25-Unit Diagonal and 7-Unit Width

Question

The rectangle ABCD is shown below.

$BD=25,BC=7$

Calculate the area of the rectangle.

00:00 Calculate the area of rectangle ABCD

00:04 We'll use the Pythagorean theorem in triangle BCD

00:10 We'll substitute appropriate values and solve for DC

00:18 We'll isolate DC

00:30 This is the length of DC, now that we have the sides we can calculate the area

00:37 Multiply length(7) by width(24)

00:44 And this is the solution to the problem

We will use the Pythagorean theorem in order to find the side DC:

$(BC)^2+(DC)^2=(DB)^2$

We begin by inserting the existing data into the theorem:

$7^2+(DC)^2=25^2$

$49+DC^2=625$

$DC^2=625-49=576$

Finally we extract the root:

$DC=\sqrt{576}=24$

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