Please solve and explain the problem below
1 answer:
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Answer:
DE = 6 cm
Step-by-step explanation:
Let DE = x cm.
Since DE is parallel to AB therefore by the alternate interior angles theorem, m∠BAD = m∠ADE and m∠ABE = m∠DEB ............(1)
As AD is an angle bisector of ∠A, therefore m∠EAD = m∠DAB ; Since BE is an angle bisector of ∠B ⇒ m∠ABE = m∠EBD.
Therefore, from (1) We get , m∠EAD = m∠ADE and m∠EBD = m∠BED.
So, the triangles ADE and EDB are then isosceles with AE = ED and ED = DB.
So AE = DE = DB = x, and since the perimeter of ABDE is 30 cm, then
12 + x + x + x = 30
⇒ 12 + 3x = 30
⇒ x = 6
Hence, the length of DE is 6 cm.
Answer:
Given the compound inequality:
Let's find the equivalent form of the inequality.
To find the equivalent form, let's simplify the inequality.
SInce it is a compund inequality, we are to seperate the inequalities.
Simplify the first two inequalities, then simplify the last two inequalities.
We have:
First two inequalities: -44 > -2x - 8
Last two inequalities: -2x - 8 ⩾ -8
Let's simplify both
Therefore, the equivalent form is:
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