What is the length of a diagonal of a square if its area is 98 square feet?

2 Answers
Aug 6, 2018

Answer:

#" "#
Length of the diagonal is #color(blue)(14# feet (approximately)

Explanation:

#" "#
Given:

A square #ABCD# with area of #color(red)(98# square feet.
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What do we need to find?

We need to find the length of the diagonal.

Properties of a Square:

  1. All the magnitudes of sides of a square are congruent.

  2. All the four internal angles are congruent, angle = #90^@#

  3. When we draw a diagonal, as is shown below, we will have a right triangle, with the diagonal being the hypotenuse.

enter image source here

Observe that #BAC# is a right triangle, with the diagonal #BC# being the hypotenuse of the right triangle.

#color(green)("Step 1":#

We are given the area of the square.

We can find the side of the square, using the area formula.

Area of a square: #color(blue)("Area = " "(Side)"^2#

#rArr "(Side)^2=98#

Since all the sides have equal magnitudes, we can consider any one side for the calculation.

#rArr (AB)^2=98#

#rArr AB=sqrt(98)#

#rArr AB~~9.899494937#

#rArr AB~~9.9# units.

Since all the sides are equal,

#AB=BD=CD=AD#

Hence, we observe that

#AB~~9.9 and AC=9.9# units

#color(green)("Step 2":#

Consider the right triangle #BAC#

Pythagoras Theorem:

#(BC)^2 = (AC)^2+(AB)^2#

#(BC)^2=9.9^2 + 9.9^2#

Using the calculator,

#(BC)^2=98.01+98.01#

#(BC)^2=196.02#

#BC=sqrt(196.02#

#BC~~14.00071427#

#BC~~14.0#

Hence,

the length of the diagonal (BC) is approximately equal to #color(red)(14 " feet."#

Hope it helps.

Aug 6, 2018

Answer:

14

Explanation:

The side is the square root of the area

# S xx S = A#

S = # sqrt 98#

The diagonal is the hypotheus of a right triangle formed by the two sides so

# C^2 = A^2 + B^2#

Where C = the diagonal A = # sqrt 98# , B = #sqrt 98#

so # C^2 = (sqrt 98)^2 + (sqrt 98)^2 #

this gives

# C^2 = 98 + 98 # or

# C^2 = 196#

# sqrt C^2 = sqrt 196#

# C = 14 #

The diagonal is 14