AD = √372 = 19.3 units
Step-by-step explanation:
If we find the length of the diagonal, using the property of the rectangles, that is diagonals bisect each other.
So DE = EB
4x+ 1 = 12x - 31
Grouping the terms, we will get
12x - 4x = 31+ 1
8x = 32
x= 32/8 = 4
Now we can find the length of the diagonal as,
DE + EB = (4(4) +1) + (12(4) - 31)
= (16+1) + (48-31)
= 17+ 17 = 34 units.
Now we can find the height.
Diagonal is equal to the sqrt of the sum of squares of width and height.
34 = √(CD²+ AD²)
Squaring on both sides, we will get,
34² = (√(CD²+ AD²))²
1156 = CD²+ AD²
1156 = 28² + AD²
1156 = 784 + AD²
1156 - 784 = AD²
372 = AD²
AD = √372 = 19.3 units
